Bissoy.com
Doctors Medicines MCQs Q&A

In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?

In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together? Correct Answer 50400

In the word 'CORPORATION', we treat the vowels OOAIO as one letter.
Thus, we have CRPRTN (OOAIO).
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Number of ways arranging these letters = $$\frac{{7!}}{{2!}}$$ = 2520
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in $$\frac{{5!}}{{3!}}$$ = 20 ways
∴ Required number of ways = (2520 x 20) = 50400

Related Questions

In the following question, two statements are numbered as I and II. On solving these statements, we get quantities I and II respectively. Solve for the both quantities and choose the correct option. Quantity I – In how many ways letters of MOBILE can be arranged when vowels are always together. Quantity II – In how many ways letters of MONDAY can be arranged when vowels are not together.
Questions below followed by three quantities. Find the relationship between them. Quantity I: In how many ways the letter of the word ‘MANUAL’ can be arranged so that vowels come together? Quantity II: Find the number of ways of forming a five number Team for a project from a group of 6 workers and 5 managers such that no odd numbers of managers are selected in the project? Quantity III: The letters of the word NATURE are to be arranged so that three vowels should not come together. Find the number of arrangement.
The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. An 8-letter word has no repetitive letter. Find the number of vowels in the word. I) No. of ways in which the consonants can be arranged is 720. II) No. of ways in which the vowels can be arranged is 2. III) 10080 different words can be formed keeping the vowels together.
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: In how many ways can the word ‘DISTURBANCE’ be arranged such that all the consonants are always together? Quantity B: In how many ways can the word ‘DISTURBANCE’ be arranged such that all the vowels are always together?
In how many different ways can the letters of the word 'CORPORATION' be arranged sothat the vowels always come together
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and chose the correct option. Quantity A: In how many different ways can the letters of the word JUMBLE be arranged? Quantity B: In how many different ways can the letters of the word BOTTLE  be arranged?
A 10-letter word is made up of 4 vowels and remaining consonants, out of which one consonant is twice present in the word. How many different words can be formed using the letters of the word, such that the vowels always come together?
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?